The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  0  1  1  X  1  1  1  1  1  1  1  1  1  1  0  1  1  1 2X  1  X  1  X  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1  1  1  1  1  1  1 4X  1  1 3X  1  1  1 2X  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  2  4  3 3X+1  0  2  1  3 3X+4  0 3X+1 3X+4  1  2  3  1  2 3X+4  0 3X+1  3 X+3 X+2  X 3X+4 3X+1  1  X 2X+2 2X+4  1 2X+4  1 4X+1  1 X+3  2 3X+4 3X X+1 2X+1 4X X+3  1 X+2 4X+1  X  1 2X+4  3 X+2 X+2  0 2X 4X+3 3X+2 3X+1 2X+1  1 X+3 X+2  1  2 4X+3 3X  1 3X+1 X+3  0 2X  X  X 4X+2 X+2 4X+4 X+2 2X+1 3X+2  3
 0  0 3X  0  0  0  0  X 2X 3X 2X 3X 2X 4X  0 2X 2X 2X 2X 3X  X 2X  0 2X 2X 3X 3X  X  X 3X 4X 3X  0  X 4X  X 2X 2X 4X  0 3X  0  X 4X 4X 4X 2X 4X 2X 4X  X 2X 4X  0  0 2X  0 4X 3X 4X 4X  0  0 4X 3X 2X 3X 2X 2X  X 2X 2X 4X  0 4X  0  0  0 2X 2X 4X 4X
 0  0  0  X  0  X 3X 3X  0 2X 2X 4X 2X 2X 3X  0 2X  X  X  X  0 4X 3X 4X  0 3X 3X  X 3X  0 3X  X 4X  X  X 2X 3X 3X  X 4X  0 2X 2X 2X 4X 4X 4X 3X 3X  0  0  0 4X  0 4X  X 4X 2X  0  X  X  X 2X 4X  X  0  X 2X 3X  0  X  0 3X  0 3X 2X  X 4X  0 4X 4X  X
 0  0  0  0 3X 3X 2X 4X 4X  X 4X 4X 2X  0  0  0 3X 2X 3X 2X  X 2X  X  X  X  0 4X 4X  X  X 3X  X  X  X  X 2X  X 2X  0 4X 4X 4X 4X 3X 4X 2X  0 2X 3X 4X  X  0 3X 3X 3X  X  X  0 2X  0 4X 3X  X 3X 4X  0 4X  X 3X  X  0  X  X  X 4X  0 4X  0 2X  X  0 4X

generates a code of length 82 over Z5[X]/(X^2) who´s minimum homogenous weight is 305.

Homogenous weight enumerator: w(x)=1x^0+228x^305+20x^306+20x^308+220x^309+900x^310+1140x^311+440x^313+960x^314+1364x^315+3160x^316+1200x^318+1540x^319+2176x^320+5540x^321+2300x^323+2460x^324+2792x^325+7840x^326+3700x^328+2660x^329+2908x^330+11120x^331+3580x^333+2840x^334+2892x^335+6800x^336+1260x^338+1500x^339+1520x^340+1880x^341+320x^344+352x^345+124x^350+136x^355+108x^360+56x^365+32x^370+28x^375+8x^380

The gray image is a linear code over GF(5) with n=410, k=7 and d=305.
This code was found by Heurico 1.16 in 15.2 seconds.